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Extremal behavior of pMAX processes
Institution:1. Department of Mathematics, University of Beira Interior, Covilhã, Portugal;2. Center of Mathematics of Minho University, Braga, Portugal;1. Department of Statistics, Central China Normal University, Wuhan 430079, China;2. Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt;1. Department of Mathematics & Statistics, University of Ottawa, 585 King Edward, Ottawa ON K1N 6N5, Canada;2. School of Mathematics & Statistics, University of Sydney, NSW 2006, Australia;1. Department of Statistics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, Republic of Korea;2. Department of Mathematics and Statistics, Lederle Graduate Research Tower, Box 34515, University of Massachusetts Amherst, Amherst, MA, USA;3. Institute of Economic Research, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, Republic of Korea;1. Department of Statistics, Amirkabir University of Technology, Tehran, Iran;2. School of Mathematics, University of Manchester, Manchester, UK
Abstract:The well-known M4 processes of Smith and Weissman are very flexible models for asymptotically dependent multivariate data. Extended M4 of Heffernan et al. allows to also account for asymptotic independence. In this paper we introduce a more general multivariate model comprising asymptotic dependence and independence, which has the extended M4 class as a particular case. We study properties of the proposed model. In particular, we compute the multivariate extremal index, tail dependence and extremal coefficients.
Keywords:Multivariate extreme value theory  Tail dependence  Extremal coefficient  Asymptotic independence
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